fmks and you

Are you interested in implementing fmks and/or reading the standard afd-fluid-representation primitives into your program? If so, take a look through the example below. It provides some numbers that you can use to crosscheck your code.

dump data comprehension

The numbers for the following example are drawn from zone i,j,k=11,12,13 of dump 1200 of the MAD a+0.9375 384x192x192 IHARM3D run.

At this location

x1 = 0.3978299442843154
x2 = 0.06510416666666666
x3 = 0.4417864669110646

Further, suppose (or verify) that the U and B primitives are given by

U1,U2,U3 =  0.4553683,  0.0147898,  0.7197036
B1,B2,B3 =  3.6612415,  0.2197483, -5.5480947

For this run, metric parameters are set to

Rin = 1.2175642950007606
Rout = 1000.0
mks_smooth = 0.5
hslope = 0.3
poly_alpha = 14.0
poly_xt =  0.82

At this location and with these metric parameters, then

poly_norm = 0.7578173169894967
r,h,p (in KS) = 1.488590864996909, 0.7666458987406977, 0.4417864669110646
gcov = [[ 0.11428415,  1.65871321,  0.        , -0.5027359 ],
        [ 1.65871321,  4.8045105 , -2.82071735, -1.41998137],
        [ 0.        , -2.82071735, 66.60209297,  0.        ],
        [-0.5027359 , -1.41998137,  0.        ,  1.71620473]]
gcon = [[-2.11428415e+00,  7.48549636e-01,  3.17024113e-02, -4.28728014e-17],
        [ 7.48549636e-01,  1.98677175e-02,  8.41433249e-04,  2.35714628e-01],
        [ 3.17024113e-02,  8.41433249e-04,  1.50501794e-02,  9.98293464e-03],
        [-1.42468631e-17,  2.35714628e-01,  9.98293464e-03,  7.77710464e-01]]

NOTICE that the components of the co- and contra-variant metric are written in fmks. If you do your calculations in KS/BL/..., you will need to transform the above values.

The U and B primitives then resolve to

ucon = [  2.02058894, -0.26000907, -0.01550771,  0.71970361 ]
ucov = [ -0.56218003,  1.12413841, -0.29943404,  0.58854419 ]
bcon = [  0.78464317,  1.71099976,  0.10273258, -2.46630283 ]
bcov = [  4.16762915,  12.7343388,  2.01595804, -7.05673667 ]

As in the metric components above, notice that these components are written in fmks. Please remember to transform as needed.